At any point in history was "Why cannot...?" used as frequently as "Why can't...?" Is it even grammatically correct to say "Why cannot you do this?" I know it can be rearranged to be "Why can you not do this?," but I always presumed the contraction and the contracted phrase could be used equivalently, without changing the sentence structure. I think this pattern holds true with the other question words (e.g. how, when, etc.); however, I also know it is common to say "Who cannot do this?" In general, are there rules pertaining to the uses of contractions in questions?

In general, I think it's best to think of contractions as independent words of their own with their own syntactic rules. In most cases, you can replace a contraction with the expansion and vice-versa, but not always.
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nohat♦Dec 1 '11 at 20:23

@nohat: I don't know how widespread the term grammaticalisation is (I only came across it myself a couple of days ago), but it seems to me this is what you mean when you say contractions can be seen as "independent words". Is that right, and if so is grammaticalisation a suitable term for this phenomenon?
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FumbleFingersDec 1 '11 at 21:46

It has never been the case that the contraction and the contracted phrase could be used equivalently. Consider, "Are you as sad as I am?" where you certainly can't use "I'm". And, of course "Don't you do that."
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David SchwartzDec 2 '11 at 0:24

@DavidSchwartz: Those just sound incorrect in the same way "Why cannot you do this?" does. If I had thought of those examples, I would ask similar questions for them.
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SWVDec 2 '11 at 0:40

2 Answers
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Note that if we substitute a pronoun (I, he, they) for "why", the transition point comes much later (1980 for "I") - or hasn't even happened yet (all other pronouns). I can't explain why that is, except by pointing out that this very sentence is an increasingly typical usage. Maybe we all tend to be a bit less formal when introducing our own selves into the text.

It's only my opinion, but I think can't (similarly, let's) are examples of grammaticalisation. The contracted form has effectively taken on a "life of its own" leading to a situation where OP is prepared to accept that there may be contexts where can't is "grammatical", but "cannot" (or the equivalent "can not") wouldn't be valid.

Using cannot / can not might be a bit stilted in many contexts now we're so used to seeing the contracted form, but I don't think it's ever ungrammatical.

At school we were taught that "can't", "let's", "it's" (for "it is", not confused with "its"), and "...'ll" are always wrong & forbidden. Well, I always had the suspection that at the school they where - old school?!
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StephenDec 1 '11 at 19:20

@FumbleFingers: It is disturbing that when I use a simple modification of your query to Google ngrams: books.google.com/ngrams/… that the cutoff point is shown to be the 1840's. I would have thought 'why can you not...' to be a more likely intermediate form. What's up with Google ngrams?
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MitchDec 1 '11 at 21:44

I forget the proper name for them, but "helper" words/verbs like can, may, be, have, get, will, would, should and so on really do have a life of their own. They're common everywhere, but particularly in speech, which might help them to "evolve" faster than, say, bog-standard nouns. But the substantive point of my answer is that can not -> cannot -> can't has led to the contracted form being seen as a free-standing syntactic unit. In the original form you could have dropped "you" into the middle of it, but now... well, you just can't.
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FumbleFingersDec 1 '11 at 22:03

1

I believe the word you are looking for is "clitic". And that's exactly right -- contractions are words in their own right. They evolve their own rules over time.
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David SchwartzDec 2 '11 at 2:39

@David: That's a new one on me. I'll remember it - if only because it's a plausible alternative to clitoric (assuming there is such a word). But I was specifically thinking of those "semi-verbs" that are often just helping the main verb along. Like "are helping" there, which could just as well be "[to] help", except we add a bit of "to be" into the mix to emphasise the ongoing nature of the activity.
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FumbleFingersDec 2 '11 at 4:05

Arnold M. Zwicky and Geoffrey K. Pullum have shown that -n't is not just a contraction of not. The two American linguists pointed out that you can say why don't you... but not *why do not you... because you can place one and only one auxiliary before the subject in an interrogative phrase. Don't is a single word while do not are two words. -n't is not a clitic but a negative inflectional suffix.

Cannot is the only negative form that contains not rather than -n't. Theoretically, since it is a single word, you can say why cannot you... without a problem. My theory is that modern English speakers don't want to put cannot before the subject because it contains not and sounds like can not. You definitely cannot say why can not you... with a separate not. On the contrary can't remains a single word, which is why they use it more and more often.

There was a time (in the 1700s) when why do not you was not uncommon. I don't know whether it was just in the written language (as an incorrect expansion of why don't you) or whether people actually said it. It sounds terrible today.
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Peter Shor Jul 19 '12 at 2:49